| Issue |
ESAIM: M2AN
Volume 59, Number 5, September-October 2025
|
|
|---|---|---|
| Page(s) | 2613 - 2637 | |
| DOI | https://doi.org/10.1051/m2an/2025063 | |
| Published online | 17 September 2025 | |
Using curved meshes to derive a priori error estimates for a linear elasticity problem with robin boundary conditions
1
IMB, UMR 5251, Univ. Bordeaux, 33400 Talence, France
2
Inria Bordeaux Sud-Ouest, Team MEMPHIS, 33400 Talence, France
* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
16
December
2024
Accepted:
5
July
2025
This work concerns the numerical analysis of the linear elasticity problem with a Robin boundary condition on a smooth domain. A finite element discretization is presented using high-order curved meshes in order to accurately discretize the physical domain. The primary objective is to conduct a detailed error analysis for the elasticity problem using the vector lift operator, which maps vector-valued functions from the mesh domain to the physical domain. Error estimates are established, both in terms of the finite element approximation error and the geometric error, respectively associated to the finite element degree and to the mesh order. These theoretical a priori error estimates are validated by numerical experiments in 2D and 3D.
Mathematics Subject Classification: 74S05 / 65N15 / 65N30 / 65G99
Key words: Linear elasticity problem / Robin boundary condition / Lagrange finite element method / high order curved meshes / geometric error / a priori error estimates
© The authors. Published by EDP Sciences, SMAI 2025
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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